Define phase of S.H.M. Show variation of displacement, velocity and acceleration with phase for a particle perfoming linear S.H.M. graphically, when it starts from extreme position.
A body starts rotating from rest. Due to a couple of `20 Nm` it completes `60` revolutions in one minute. Find the moment of inertia of the body.

Explanation

Phase of S.H.M. : The physical quantity which describes the state of oscillation of the particle perfoming S.H.M. i.e., it gives the displacement of the particle and its direction of motion from its equilibrium position.
In the equation of S.H.M.,
`x=Asin(omegat+phi)`
where, `(omegat+phi)` is the phase angle of S.H.M.
Graphical representation of S.H.M. starting from extreme position:

Numerical :
Given : Couple `(tau)=20Nm`,
`n=60` rev in `1 atm 1 min=1 r.p.s`
`t=1min=60sec`
Now, `theta=omegat=2pint`
`:. theta=2pixx1xx60=120pi`
Now, `theta=omega_(0)t+(1)/(2)alphat^(2)`
`120pi=0+(1)/(2)alpha(60^(2))` [`:'omega_(0)=0`]
`alpha=(240pi)/(60xx60)`
`=(pi)/(15)rad//s^(2)`
As we know, `I=(tau)/(alpha)`
`I=(20)/((pi)/(15))`
`=(15xx20)/(pi)`
`=95.48 kg m^(2)`